Question

1) (2⁸•7⁹)/( 14¹⁰)•(26⁵•2¹⁰)/( 13⁶•8⁴)
2) (12⁵)/(2³•4⁴)
3) (2⁸•7⁹)/(14¹⁰):(26⁵)/(13⁶•8⁴)
4) (12⁵)/(2³•3⁴)•(10⁵)/(2⁶•5⁷)

Answer 1

$1) frac{2^8cdot 7^9}{14^{10}} cdot frac{26^5cdot 2^{10}}{13^6cdot 8^4} =frac{2^8cdot 7^9}{(2cdot7)^{10}} cdot frac{(2cdot 13)^5cdot 2^{10}}{13^6cdot (2^3)^4} = \ \= frac{1}{2^2cdot7} cdot frac{2^5cdot 13^5cdot 2^{10}}{13^6cdot 2^{12}} = \ \ = frac{2^{5+10}cdot 13^5}{2^{2+12}cdot 13^6cdot 7^{10}} = frac{2}{7cdot 13}=frac{2}{91}$

$2) frac{12^5}{2^3cdot 4^4}= frac{(3cdot 4)^5}{2^3cdot 4^4}= frac{3^5cdot 4^5}{2^3cdot 4^4}= frac{3^5cdot 4}{8}= frac{3^5}{2}= frac{243}{2}$

$3) frac{2^8cdot 7^9}{14^{10}} : frac{26^5}{13^6cdot 8^4} =frac{2^8cdot 7^9}}{(2cdot7)^{10}} : frac{(2cdot 13)^5}{13^6cdot (2^3)^4} =frac{2^8cdot 7^9}{2^{10}cdot7^{10}} :frac{2^5cdot 13^5}{13^6cdot 2^{12}} = \ \ =frac{1}{2^2cdot7} cdotfrac{13cdot 2^7}{1} = frac{2^{5}cdot 13}{7}=frac{416}{7}$

$4) frac{12^5}{2^3cdot 3^4}cdot frac{10^5}{2^6cdot 5^7} = frac{(3cdot 4)^5}{2^3cdot 3^4}cdot frac{(2cdot 5)^5}{2^6cdot 5^7} = frac{3^5cdot 4^5}{2^3cdot 3^4}cdot frac{2^5cdot 5^5}{2^6cdot 5^7}= frac{3cdot 2^7}{2cdot 5^2}= frac{384}{50}= frac{768}{100}= \ \ =7,68$